KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 2 Mathematics
A carpenter constructed a closed wooden box with internal measurements 1.5 metres long, 0.8 metres wide and 0.4 metres high. The wood used in constructing the box was 1.0 cm thick and had a density of 0.6 gcm3.
(a) Determine the: (i) volume, in cm3, of the wood used in constructing the box; (ii) mass of the box, in kilograms, correct to 1 decimal place. (b) Identical cylindrical tins of diameter 10 cm, height 20cm with a mass of 120 g each were packed in the box. Calculate the: (i) maximum number of tins that were packed; (ii) total mass of the box with the tins.
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Form 1 Mathematics
A saleswoman is paid a commission of 2% on goods sold worth over Ksh 100 000. She is also paid a monthly salary of Ksh 12 000. In a certain month, she sold 360 handbags at Ksh 500 each.
(a) Calculate the saleswoman’s earnings that month. (b) The following month, the saleswoman’s monthly salary was increased by 10%. Her total earnings that month were Ksh 17 600. Calculate: (i) the total amount of money received from the sales of handbags that month; (ii) the number of handbags sold that month. Form 2 MathematicsForm 3 MathematicsForm 2 Mathematics
A cylindrical solid whose radius and height are equal has a surface area of 154 cm2. Calculate its diameter, correct to 2 decimal places. (Take π = 3.142)
Form 3 Mathematics
Given that 3θ is an acute angle and sin 3θ = Cos 2θ°, find the value of θ.
Form 1 Mathematics
A fruit vendor bought 1948 oranges on a Thursday and sold 750 of them on the same day.On Friday, he sold 240 more oranges than on Thursday. On Saturday he bought 560 more oranges. Later that day, he sold all the oranges he had at a price of Ksh 8 each.
Calculate the amount of money the vendor obtained from the sales of Saturday. Form 1 Mathematics
Using a ruler and a pair of compasses only, construct a rhombus QRST in which angle TQR = 600 and QS = 10 cm.
Form 1 MathematicsForm 3 MathematicsForm 1 Mathematics
A Kenyan company received US Dollars 100 000. The money was converted into Kenya shillings in a bank which buys and sells foreign currencies as follows:
Buying Selling (in Kenya shillings) (in Kenya shillings) 1 US Dollar 77.24 77.44 1 Sterling Pound 121.93 122.27 (a) calculate the amount of money, in Kenya shillings, the company received. (b) The company exchanged the Kenya shillings calculated in (a) above, into sterling pounds to buy a car from Britain. Calculate the cost of the car to the nearest sterling pound. Form 1 Mathematics
The sum of three consecutive odd integers is greater than 219. Determine the first three such integers.
Form 2 Mathematics
A bus left a petrol station at 9.20 a.m. and travelled at an average speed of 75 km/h to a town N. At 9.40 a.m. a taxi, travelling at an average speed of 95 km/h, left the same
petrol station and followed the route of the bus. Determine the distance, from the petrol station, covered by the taxi at the time it caught up with the bus. Form 2 Mathematics
A straight line l passes through the point (3, —2) and is perpendicular to a line whose equation is 2y-4x= 1.
Find the equation of l in the form y = mx + c, where m and c are constants. Form 1 Mathematics
Kutu withdrew some money from a bank. He spent 3/8 of the money to pay for Mutua’s school fees and 2/5 to pay for Tatu’s school fees. If he remained with Ksh 12 330, calculate the amount of money he paid for Tatu’s school fees.
Form 3 Mathematics
a) On the grid provided, draw a graph of the functionY= ½ x2 – x + 3 for 0 ≤ x ≤ 6
b) Calculate the mid-ordinates for 5 strips between x= 1 and x=6, and hence Use the mid-ordinate rule to approximate the area under the curve between x= 1, x=6 and the x-axis. c) Assuming that the area determined by integration to e the actual area, calculate the percentage error in using the mid-ordinate rule. Form 1 Mathematics
Three points P, Q and R are on a level ground. Q is 240 m from P on a bearing of 2300 . R is 120 m to the east of P
a) Using a scale of 1 cm to represent 40 m, draw a diagram to show the positions of P, Q and R in the space provided below. b) Determine i) The distance of R from Q ii) The bearing of R from Q c) A vertical post stands at P and another one at Q. A bird takes 18 seconds to fly directly from the top of the post at q to the top of the post at P. Given that the angle of depression of the top of the post at P from the top of the post at Q is 90, Calculate: i) The distance to the nearest metre, the bird covers; ii)The speed of the bird in Km/h Form 3 Mathematics
The diagram below shows the speed-time graph for a train traveling between two stations. The train starts from rest and accelerates uniformly for 150 seconds. It then travels at a constant speed for 300 seconds and finally decelerates uniformly for 200 seconds.
Given that the distance between the two stations is 10 450 m, calculate the:
a) Maximum speed, in Km/h, the train attained; b) Acceleration, c) Distance the train traveled during the last 100 seconds; d) Time the train takes to travel the first half of the journey. Form 2 Mathematics
A glass, in the form of a frustum of a cone, is represented by the diagram below.
The glass contains water to a height of 9 cm,. The bottom of the glass is a circle of radius 2 cm while the surface of the water is a circle of radius 6 cm.
a) Calculate the volume of the water in the glass
b) When a spherical marble is submerged into the water in the glass, the water level rises by 1 cm. Calculate: i) The volume of the marble; ii) The radius of the marble Form 3 MathematicsForm 3 Mathematics
A school planned to buy x calculators for a total cost of Kshs 16 200. The supplier agreed to offer a discount of Kshs 60 per calculator. The school was then able to get three extra calculators for the same amount of money.
a) Write an expression in terms of x, for the: i) Original price of each calculator. ii) Price of each calculator after the discount b) Form an equation in x and hence determine the number of calculators the School bought. c) Calculate the discount offered to the school as a percentage |
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